原子集校正及步长可控的稀疏度未知CS重构  

Atom Set Calibration and Step Control for Unknown-Sparsity Reconstruction from Compressive Sensing

作　　者：曾春艳[1,2] 马丽红[1] 杜明辉[1] 

机构地区：[1]华南理工大学电子与信息学院,广州510641 [2]湖北工业大学电气与电子工程学院,武汉430068

出　　处：《应用科学学报》2014年第2期163-169,共7页Journal of Applied Sciences

基　　金：国家自然科学基金(No.60972133;No.U0735004);广东省自然科学基金团队项目基金(No.9351064101000003);广东省能源技术重点实验室项目基金(No.2008A060301002);湖北工业大学博士科研启动基金(No.BSQD13037)资助

摘　　要：对残差信号用类高斯分布建模,通过分析回溯型自适应正交匹配追踪(backtracking-based adaptive orthogonal matching pursuit,BAOMP)算法的阈值选择方法与常规信号稀疏度方法的一致性和差异,提出一种改进的BAOMP算法.采用80–20准则判断信号的粗匹配状态,然后对后续匹配步骤引入可变步长阈值,实现选入原子集容量的精细调整,提高选入原子的正确匹配率,避免了残差信号的准周期性失配.实验结果表明,与BAOMP算法相比,在500次重复实验中,改进的BAOMP算法对高斯稀疏信号的精确重建概率提高17%～26%,对自然图像的精确重建概率提高70%以上.This paper models residual signals with Gaussian-like distributions, based on which consistency between the Backtracking-based adaptive orthogonal matching pursuit （BAOMP） threshold and signal sparse- level is analyzed. An improved BAOMP （IBAOMP） method is thenproposed. Themethod estimates the preliminary matching state usingthe 80-20 rule, and introduces a threshold with variable step size to subtly adjust atom set to raise the correct rate of selected atoms and avoid quasi-periodic mismatches of residual signals. Simulation results of 500 tests show that the exact recovery probability of IBAOMP is 17%～26% higher than BAOMP for Gaussian sparse signals, and more than70% higher than BAOMP for natural images.

关 键 词：压缩感知 正交匹配追踪 匹配集裁剪 增量步长控制 

分 类 号：TN911.7[电子电信—通信与信息系统]